Which of the following numbers is a multiple of 2? ${51,79,83,86,109}$
Explanation: The multiples of $2$ are $2$ $4$ $6$ $8$ ..... In general, any number that leaves no remainder when divided by $2$ is considered a multiple of $2$ We can start by dividing each of our answer choices by $2$ $51 \div 2 = 25\text{ R }1$ $79 \div 2 = 39\text{ R }1$ $83 \div 2 = 41\text{ R }1$ $86 \div 2 = 43$ $109 \div 2 = 54\text{ R }1$ The only answer choice that leaves no remainder after the division is $86$ $ 43$ $2$ $86$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $86$ $86 = 2\times43 2 = 2$ Therefore the only multiple of $2$ out of our choices is $86$. We can say that $86$ is divisible by $2$.